# Monotonic piecewise cubic interpolation, with applications to ODE plotting

D.J. Higham

Research output: Contribution to journalArticle

19 Citations (Scopus)

### Abstract

Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.
Original language English 287-294 7 Journal of Computational and Applied Mathematics 39 3 https://doi.org/10.1016/0377-0427(92)90205-C Published - 8 May 1992

### Fingerprint

Monotonic
Interpolation
Interpolate
Knot
Monotonicity
Interpolants
Approximate Solution
Derivatives
Derivative
Necessary
Drawing

### Keywords

• Cubic polynomial
• Hermite
• interpolation
• monotonicity
• initial-value problem
• numerical mathematics

### Cite this

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title = "Monotonic piecewise cubic interpolation, with applications to ODE plotting",
abstract = "Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.",
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In: Journal of Computational and Applied Mathematics, Vol. 39, No. 3, 08.05.1992, p. 287-294.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Monotonic piecewise cubic interpolation, with applications to ODE plotting

AU - Higham, D.J.

PY - 1992/5/8

Y1 - 1992/5/8

N2 - Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.

AB - Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.

KW - Cubic polynomial

KW - Hermite

KW - interpolation

KW - monotonicity

KW - initial-value problem

KW - numerical mathematics

UR - http://dx.doi.org/10.1016/0377-0427(92)90205-C

U2 - 10.1016/0377-0427(92)90205-C

DO - 10.1016/0377-0427(92)90205-C

M3 - Article

VL - 39

SP - 287

EP - 294

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 3

ER -